Showing papers on "Periodic graph (geometry) published in 1997"
TL;DR: The behavior of the powers of a matrix over is studied and a representation of the complete sequence (Am)m∈ℕ which can be computed within polynomial time complexity is computed.
Abstract: Consider the extremal algebra
=(ℝ∪{∞},min,+), using + and min instead of addition and multiplication. This extremal algebra has been successfully applied to a lot of scheduling problems. In this paper the behavior of the powers of a matrix over
is studied. The main result is a representation of the complete sequence (A
m
)
m∈ℕ which can be computed within polynomial time complexity. In the second part we apply this result to compute a minimum cost path in a 1-dimensional periodic graph.
35 citations
07 Jul 1997
TL;DR: In the non-periodic case a simple algorithm is presented to determine whether a graph has a potential satisfying the min-max equations and some results regarding the uniqueness of solutions in the latter case are given.
Abstract: In this paper we address min-max equations for periodic and non-periodic problems. In the non-periodic case a simple algorithm is presented to determine whether a graph has a potential satisfying the min-max equations. This method can also be used to solve a more general quasi periodic min-max problem on periodic graphs. Also some results regarding the uniqueness of solutions in the latter case are given.
1 citations